Question

Debbie and Trisha are looking at the equation the square root of the quantity of 4 times x minus 6 equals square root of x . Debbie says that the solution is extraneous. Trisha says that the solution is non-extraneous. Is Debbie correct? Is Trisha correct? Are they both correct? Justify your response by solving this equation, explaining each step with complete sentences.

Answer 1

@radar

Answer 2

Well, they can't possibly be both correct, since they pretty much contradict each other, so it has to be one or the other.

\[\Large \sqrt{4x-6}=\sqrt x\]
How did you go about solving this? :)

Answer 3

idk thats the promblem

Answer 4

@terenzreignz

Answer 5

Well, the radical signs (square roots) sort of screw things up, so why don't you square both sides of the equation to get rid of them?
\[\Large \sqrt{p}^2=p\]

Answer 6

so we sqare both sides?

Answer 7

Yup.

Answer 8

Then solve for x.

Answer 9

@terenzreignz

Answer 10

@radar

Answer 11

What did you get when you squared both sides ?

Answer 12

ok lets write equation on left hand side
square root of the quantity of 4 times x minus 6
first write without squareroot
4 times x= 4x and subtract 6 now .....so
is 4x-6
now take square root
\[\sqrt{4x-6}\]